There are three components we need to add to the tweeter. A capacitor and an inductor will prevent the low frequency energy below the crossover from overwhelming the tweeter, and will shape the response near the crossover. A resistor will be used to set the overall level of the treble. The complete tweeter schematic is shown below.

The capacitor
Take the value of impedance you wrote down two posts ago (for our example it was 3.75). Multiply it by 12.6 and then multiply it by the crossover frequency. For example, 3.75 x 12.6 x 2000 equals 94500.

Now, if your calculator has an invert function, use it on this number, or simply do 1 divided by your answer. ie: 1/94500 is 10.6uF which is close enough to 10uF.

The inductor
Take the value of impedance and divide this by the result you get when you multiply the crossover frequency by 3.15

For example, 3.75/(2000 x 3.15) which equals 0.000595, or 0.595m. The closest value of inductor is 0.56mH.

The resistor
If you subtract the woofer sensitivity figure from the tweeter sensitivity figure, you'll have a starting point for how much to lower the tweeter's level. Lower it a couple of dB more for good measure, if desired (there are several reasons for wanting to try this).

To choose the value of resistor to use, look at the following. To attenuate the tweeter by 1dB, take the tweeter impedance value we've been using here and multiply it by 0.12 to get the resistor value. For 2dB multiply instead by 0.25, 3dB by 0.4, 4dB by 0.6, 5dB by 0.8, and finally for 6dB of attenuation use a resistor which is equal to the impedance value.

You'll likely tweak this later, it is a very commonly adjusted component.

Polarity
One final point is the polarity of the tweeter. Try reversing the connections and listen each way. There will be more on why in the next post.

Finally
The entire response is shown below (image 2). It is a good starting point and will be tweaked later.

Note -- This section is slightly technical and may be skipped over if desired.

Phase
A speaker cone moves back and forth in cycles. Each cycle is analysed as a rotation. Phase is an indicator of a point in that rotation, and is measured in degrees. It is important to consider phase because where you have two drivers sharing the crossover region, they need to work together. If one is moving out when the other is moving in they will cancel each other to some degree and the direct sound will not be balanced around the crossover region.

I put this section before the tweaking sections to create awareness as every crossover change you make is going to affect phase to some extent and to put it simply, this may cause unexpected results in the frequency response. For now, it is enough to just be aware of this fact.

With regards to the polarity of the tweeter, which is simply the order that the positive and negative wires are connected, both ways should be tried on each speaker designed this way. As there are only two ways it can be, it is a broad kind of tweak but we need to find which is best.

As an experimental tweak you can do if there seems to be a problem in blending the tweeter to the woofer, and in keeping with our trial and error approach… it may be worth changing one of the major components, either the woofer inductor or the tweeter capacitor, then alter the other driver's crossover to match up. For example, increasing the tweeter's capacitor a little and then increasing the woofer's inductor by a similar amount will push the crossover lower but shouldn't necessarily change the balance. The point is that the difference in phase between the drivers may have changed which may have altered how well they blend.

Diffraction
For our purposes, diffraction is when sound encounters a change in direction. For example, if sound is travelling sideways across the baffle and it reaches the edge, it will expand to reach around the sides. This produces a new (and normally unwanted) wave in return, which is out of phase and out of time with the original sound.

There is sometimes confusion between this and baffle step diffraction although they are about the same phenomenon. The baffle step shows a specific and easily measureable effect that gets its share of attention. Diffraction in general tends to be a less easily identifiable source of problems that should be dealt with by reducing or treating sharp edges where possible.

Diffraction is the reason that drivers are sometimes flush mounted (sunk into the baffle), and why the ratio of baffle height to width and driver placement on it, is considered. Cabinet edges ought to be rounded as well.

There are three components in the woofer crossover. Between them, there is plenty of room for adjustment. Since the resistor and capacitor are doing a specific job of fixing the impedance, the inductor may seem to be the component that ought be adjusted first, but as we will see there are no hard and fast rules here.

Fixing our example system
Although we won't see what's going on if we don't measure it, we can still hear it. The top half of image 1 shows the starting crossover, and it has a small peak at around 1kHz which I will use to illustrate the point. I decided to increase the value of the inductor (to 1mH) to bring down the woofers response near the crossover.

Adjusting the inductor
Making the inductor larger will reduce the upper midrange by cutting off the woofer at a lower frequency (image 2). This can help to tame some kinds of harshness, or to give the impression of more bass. It is useful for when the woofer is too loud at its top end to begin with so if it sounds better, do it. Be aware however that the desire to turn up the bass is sometimes the result of room based cancellations which have little to do with the crossover.

Going the other way with the inductor can give the bass more punch by increasing the level of bass harmonics. On the other hand if your tweeter isn't blending, it may be because the woofer is not meeting it at the crossover (not producing enough upper midrange, for example), so reducing the inductor value might help.

Adjusting the resistor
Reducing this resistance should increase the woofer's output near the crossover without changing the crossover frequency (image 3). This causes the woofer crossover to more closely resemble a second order filter. In practice, adjusting the resistor gives somewhat similar effects to the control you get with small changes in the size of the inductor, but there will be differences between the two in response and phase. With a no-measure type of crossover you should try both if necessary, as one may work better than the other.

Adjusting the capacitor
Also affects the region just below the crossover, and changes the frequency of the crossover. If you found that you had too much upper midrange but increasing the inductance made the sound too dull, increasing the capacitance value is worth a try instead.

With and without having flattened the impedance
The fourth image below shows the woofer response when using the inductor before fixing the impedance (light blue). Green shows the proper crossed over response and grey is the raw woofer response for reference. It is obvious that without the resistor and capacitor, the response is not following the same downward trend. It fails to reduce the cone breakup region sufficiently (above 3kHz).

Notch filters
The fifth image shows the effect of using a notch filter to reduce the breakup region even further. Although I'll leave the design of notch filters for another time, it can be seen that one is useful in reducing the breakup region by a significant amount. It is usually good to try to have this region playing 20dB less than the rest of the spectrum. The green trace is the normal crossover and the light blue trace shows the notch filter in place. It was made using a 0.4mH inductor, a 2uF capacitor and a 3.3 ohm resistor.

Going second order
This will reduce the woofer's output above the crossover where only the tweeter should be heard. If you feel this is necessary, start reducing the value of resistance in the woofer crossover. This is likely to produce a peak in the response as discussed above and this can be offset by increasing the inductance. You will have moved closer to a second order electrical crossover.

The series resistor
This is the normal method of setting the level and is probably the first thing you'll try when sorting out treble issues. Changes to the woofer crossover may need an adjustment here as well. Changing this resistor will have the side-effect of bringing about some minor changes in the tweeter's tonal balance (image 1).

The capacitor
This will change the crossover point for the tweeter. This is a fair tweak if it gives you what you need, even if you don't do anything to the woofer. Larger capacitors will give you an increase in the response at the tweeter's lower end, and will also increase the level of the tweeter just above the crossover point (image 2).

The inductor
A larger inductor will also lower the crossover point, but it will reduce the level just above the crossover (image 3).

It may not always be clear whether to adjust the capacitor or the inductor until you try it.

The parallel resistor
Reducing this value will typically reduce the level of the tweeter (image 4). In some cases there will be an emphasis around the resonance, and top end. In some cases it will produce a better result than adjusting the other resistor, just don't use extremely small values for this one.

Don't forget to try reversing the tweeter polarity to see which way works best. This should be repeated after significant crossover adjustments.

Tweeter level
Playing a tweeter louder than it is meant to be played may sound good for a while, but can become tiring. If you find that some recordings sound a little harsh or bright, and annoying, start by reducing the level of the tweeter. When a tweeter blends, you should only just hear it, and not specifically…it shouldn't stand out.

General issues
When listening for problems, try to identify which driver is involved (if only one), and which frequency range is involved. Try to repeat the problem using different types of music. Is it due to some range being too loud or is it some other kind of distortion. Problems due to some frequency range being too quiet tend to be more difficult to identify. Be persistent, it sometimes takes time to sort out issues like this.

Not enough bass
Problems around a lack of bass are often due to the room, not the speaker. If you have lowered the midrange and treble with the crossover, but your bass is still not satisfactory, you might try moving your speakers around and using subwoofers in an attempt to augment the room affected bass response. It is a commonly held belief that subwoofers are a poor fix for small speakers but subwoofers tend to have a special case relationship with domestic listening rooms, and are not a bad idea, even overlapping with large speakers.

If you seek more pluck, or punch to the bass lines you'll find this in the midrange, even the upper midrange which is often a matter of adjusting the woofer inductor or resistor. You might need to correct the tweeter to match.

Dealing with baffle step diffraction
This may be approached by simply increasing the inductance in the woofer circuit until it sounds right. If this lowers the midrange too much you might lower the resistor value in the woofer circuit. There should be enough control in adjusting the three woofer components in most cases to bring this issue into line, with some trial and error.

If you are specifically trying to increase the bass a little for whatever reason, you could use a circuit that is usually used for fixing baffle step issues. Place a second inductor in series with the one already in the woofer circuit, then place a resistor across (in parallel with) that inductor to limit its effect and prevent it cutting off too much midrange. The resistor should be equal to or less than the woofers nominal impedance (ie. 8 ohms for an 8 ohm woofer). I'd suggest starting with 4 ohms. Continue to listen for problems and try to correct what seems to need it. Experiment with the size of the inductor and adjust the tweeter level afterward if required.

A woofer that has been crossed over too high
Two issues here. Apart from cone breakup which has been covered, a woofer that is becoming directional might sound thin in the upper midrange, which can be worked around by reducing the resistor value in the woofer crossover and/or reducing the tweeter's capacitance and/or trying different values for the tweeter resistors.

A word on component quality
You may have heard that quality components can make a difference, and this is true to a point. A properly designed crossover using appropriate off the shelf parts will sound better than a generic crossover using the most expensive parts. You can achieve very good results using moderately priced components.

One comment on tweeter polarity. i.e. choosing the right polarity. Try pink noise and sit fairly close (and on the intended listening axis). Reverse the polarity reapeatedly. The better position will make the sound more integrated and will make the units sound like they merge. With the wrong choice the woofer and tweeter are perceived as separate and distinct units.

Excellent work AllenB! A lot of thought, time and effort has gone into producing this tutorial! Wish I had something like this 26 years ago when I first started randomly putting drivers together with pre-built crossovers!

Nice writeup! This captures many of the steps and explains things in a very basic way so that a beginner can understand it.

I wanted to let beginners know that there is a similar guide to designing speakers without measurements by Dave Dal Farra that is posted here (at the bottom of the page):Loudspeaker Design Software
It goes in to more detail about how to use various free software programs and spreadsheets as part of the design, and gives a worked example design. It might be a good next step for people who have completed a a "first" speaker design using your tutorial.